Premium
On the Injective Tensor Product of Distinguished Frechet Spaces
Author(s) -
Carlos Díaz Juan,
Domaeski Pawel
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19991980104
Subject(s) - mathematics , tensor product , injective function , tensor product of hilbert spaces , pure mathematics , product (mathematics) , space (punctuation) , tensor (intrinsic definition) , dual (grammatical number) , dual space , topological tensor product , tensor contraction , functional analysis , geometry , computer science , art , biochemistry , chemistry , literature , gene , operating system
An example of two distinguished Fréchet spaces E, F is given (even more, E is quasinormable and F is normable) such that their completed injective tensor product E ⊗ F is not distinguished. On the other hand, it is proved that for arbitrary reflexive Fréchet space E and arbitrary compact set K the space of E ‐ valued continuous functions C(K, E) is distinguished and its strong dual is naturally isomorphic to ⊗ where L 1 (μ) = C(K) 1 .